Abstract
Interpolating the exchange–correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke’s atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.
Highlights
The density-fixed adiabatic connection [1] of Kohn–Sham (KS) density functional theory (DFT) is a powerful theoretical tool for the construction of approximate exchange–correlation (XC) functionals: for example, hybrid [2] and double-hybrid functionals [3] can be constructed from simple models of the adiabatic connection integrand [4,5,6]
We analyze the kinetic correlation energy density, and how its peak in the origin, which in systems with Coulomb confinement plays an important role for strong correlation [27,28,29], varies as the system becomes more and more correlated
For comparison with traditional Density Functional Approximations (DFAs), such as the local density approximation (LDA) [41] and the PBE GGA [42], we show the error in the exchange–correlation energy Exc[ ] in the
Summary
The density-fixed adiabatic connection [1] of Kohn–Sham (KS) density functional theory (DFT) is a powerful theoretical tool for the construction of approximate exchange–correlation (XC) functionals: for example, hybrid [2] and double-hybrid functionals [3] can be constructed from simple models of the adiabatic connection integrand [4,5,6] These approximations, use exact ingredients only for the limit of small coupling strength and are biased toward the weakly correlated regime. Interpolations constructed from the global ingredients are in general computationally cheaper than their local counterpart, because they can use semilocal approximations for the strong-interaction functionals, and because they do not need energy densities from exact exchange and from secondorder perturbation theory, but only their global values. We analyze the kinetic correlation energy density, and how its peak in the origin, which in systems with Coulomb confinement plays an important role for strong correlation [27,28,29], varies as the system becomes more and more correlated
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